Journal Article10.1364/OL.30.002140
Spectral renormalization method for computing self-localized solutions to nonlinear systems
TL;DR: A new numerical scheme for computing self-localized states--or solitons--of nonlinear waveguides is proposed, which can find wide applications in nonlinear optics and related fields such as Bose-Einstein condensation and fluid mechanics.
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Abstract: A new numerical scheme for computing self-localized states—or solitons—of nonlinear waveguides is proposed. The idea behind the method is to transform the underlying equation governing the soliton, such as a nonlinear Schrodinger-type equation, into Fourier space and determine a nonlinear nonlocal integral equation coupled to an algebraic equation. The coupling prevents the numerical scheme from diverging. The nonlinear guided mode is then determined from a convergent fixed point iteration scheme. This spectral renormalization method can find wide applications in nonlinear optics and related fields such as Bose–Einstein condensation and fluid mechanics.
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Citations
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References
•Book
Nonlinear Fiber Optics
Govind P. Agrawal
- 01 Jan 1989
TL;DR: The field of nonlinear fiber optics has advanced enough that a whole book was devoted to it as discussed by the authors, which has been translated into Chinese, Japanese, and Russian languages, attesting to the worldwide activity in the field.
•Book
Solitons and the Inverse Scattering Transform
Mark J. Ablowitz,Harvey Segur +1 more
- 01 Dec 1981
TL;DR: In this paper, the authors developed the theory of the inverse scattering transform (IST) for ocean wave evolution, which can be solved exactly by the soliton solution of the Korteweg-deVries equation.
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